Assuming your only MI-source income is your wife's W-2 wages:
When you do the MI non-resident return, enter zero as the MI income. That will result in a full refund of the incorrectly withheld MI taxes.
Your wife should also file Form MI-W4 with her employer, indicating that she is exempt from MI withholding because she is a resident of Ohio, a reciprocal state. Here's a link to the form: https://www.michigan.gov/documents/taxes/MI-W4_370050_7.pdf
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
